相关论文: Optimal Moebius Transformations for Information Vi…

Li, Ma and Wang have provided in [\emph{Deformations of hypersurfaces preserving the M\"obius metric and a reduction theorem}, Adv. Math. 256 (2014), 156--205] a partial classification of the so-called Moebius deformable hypersurfaces, that…

We show that product Chebyshev polynomial meshes can be used, in a fully discrete way, to evaluate with rigorous error bounds the Lebesgue constant, i.e. the maximum of the Lebesgue function, for a class of polynomial projectors on cube,…

Generation of super-resolution (SR) ultrasound (US) images, created from the successive local-ization of individual microbubbles in the circulation, has enabled the visualization of microvascular structure and flow at a level of detail that…

This paper proposes an enhancement of convolutional neural networks for object detection in resource-constrained robotics through a geometric input transformation called Visual Mesh. It uses object geometry to create a graph in vision…

To generalize to novel visual scenes with new viewpoints and new object poses, a visual system needs representations of the shapes of the parts of an object that are invariant to changes in viewpoint or pose. 3D graphics representations…

We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how…

Metasurfaces have recently opened up applications in the quantum regime, including quantum tomography and the generation of quantum entangled states. With their capability to store a vast amount of information by utilizing the various…

We consider the common problem setting of an elastic sphere impacting on a flexible beam. In contrast to previous studies, we analyze the modal energy distribution induced by the impact, having in mind the particular application of impact…

We present a versatile formulation of the convolution operation that we term a "mapped convolution." The standard convolution operation implicitly samples the pixel grid and computes a weighted sum. Our mapped convolution decouples these…

We propose a novel optimization framework for computing the medial axis transform that simultaneously preserves the medial structure and ensures high medial mesh quality. The medial structure, consisting of interconnected sheets, seams, and…

As modeling and visualization applications proliferate, there arises a need to simplify large polygonal models at interactive rates. Unfortunately existing polygon mesh simplification algorithms are not well suited for this task because…

With the rise of mobile-first consumption, users increasingly engage with data visualizations on mobile devices. However, the vast majority of existing visualizations are originally authored for desktop environments. Due to significant…

Identifying the Bolch sphere with the Riemann sphere(the extended complex plane), we obtain relations between single qubit unitary operations and M\"{o}bius transformations on the extended complex plane.

Simulating quantum channels is a fundamental primitive in quantum computing, since quantum channels define general (trace-preserving) quantum operations. An arbitrary quantum channel cannot be exactly simulated using a finite-dimensional…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

The Multi-Objective Mixed-Integer Programming (MOMIP) problem is one of the most challenging. To derive its Pareto optimal solutions one can use the well-known Chebyshev scalarization and Mixed-Integer Programming (MIP) solvers. However,…

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…

We review the theory of, and develop algorithms for transforming a finite point set in ${\bf R}^d$ into a set in \emph{radial isotropic position} by a nonsingular linear transformation followed by rescaling each image point to the unit…

Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…